Swelling under uniaxial elongation

Eliminating 0 by using the relation (4.74), and neglecting /u./2 on the left-hand side, we find the relation between the tension and elongation as 

The ratio between the deformation parallel with and perpendicular to the tension,  

In reality, most materials have a between 0 and 1/2. For a single chain swollen in a good solvent, scaling argument leads to a = 1/4 [32]. The measurement of the ratio KIII of the swollen polyacrylamide gels [33] showed that ii takes a value between 0.26 and 0.29 depending on the preparation condition. 

For a gel swollen under tension, the Poisson ratio (4.86) is given by 

it may take negative values in a certain temperature range. When gels are stretched in the x direction, they absorb solvent molecules and enhance swelling, so that they expand in the y and z directions as well. Because they are open systems that solvent molecules can enter and leave, a negative Poisson ratio is possible. It does not contradict with the stability condition of the matter. 

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Rheological properties of filled polymers can be characterised by the same parameters as any fluid medium, including shear viscosity and its interdependence with applied shear stress and shear rate elongational viscosity under conditions of uniaxial extension and real and imaginary components of a complex dynamic modulus which depend on applied frequency [1]. The presence of fillers in viscoelastic polymers is generally considered to reduce melt elasticity and hence influence dependent phenomena such as die swell [2]. 

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